My father works and earns money in a country where he is not allowed to work because he is not a national of that country. Is his income halal or haram?
It means he is a fugitive who is earning a living. His circumstances may be that he needs to stay and earn, as someone in need. Depending on his need, he may not have any other choice and would be subjected to that kind of leniency due to necessity. (If he is there cheating the system without need, for worldly reasons, then that is unbecoming for a Muslim and not good conduct. We should strive to be honorable in everything we do).
❶ - HOWEVER, the general and scholarly ruling is as below, which basically states that it is incorrect to cheat and so on.
It is not permissible for a Muslim to betray them or cheat them. The Prophet (peace and blessings of Allaah be upon him) said: “Render back trusts to the one who entrusted you, and do not betray the one who betrays you.” Narrated by Abu Dawood, 3534; classed as saheeh by al-Albaani in Saheeh Abi Dawood.
And the Prophet (peace and blessings of Allaah be upon him) described one of the attributes of the hypocrite as being: “When he enters into a covenant, he proves treacherous.” Narrated by al-Bukhaari, 34; Muslim, 58.
The Prophet (peace and blessings of Allaah be upon him) used to send his companions to fight the mushrikeen, and one of the things he advised them was: “Do not be treacherous.” Narrated by Muslim, 1731.
Source for the above, although in a different context but still the principles apply: https://islamqa.info/en/52810
❷ - Something which you didn't ask but which seems to be an underlying reason for the question, is if you are allowed to partake of the wealth of your father and whether that is halal for you or not. Know then that if it is haram on him, it does not become haram on you.
Shaykh Ibn ‘Uthaymeen said: Some of the scholars said that in the case of wealth that is haraam because of the way in which it was acquired, the sin is only on the one who earned it, not on the one who takes it in a permissible way from the one who acquired it. This is unlike wealth that is haraam in and of itself, such as alcohol, wealth seized by force, and so on. This view has a strong basis, because the Messenger (peace and blessings of Allaah be upon him) bought food from the Jews for his family, and he ate from the lamb that the Jewish women gave him in Khaybar, and he accepted the invitation of a Jew, even though it is well known that most of the Jews consume riba and haraam wealth. Perhaps this view is further supported by the words of the Prophet (peace and blessings of Allaah be upon him) concerning the meat that was given in charity to Bareerah: “It is charity for her and a gift from her to us.” Al-Qawl al-Mufeed ‘ala Kitaab al-Tawheed, 3/112.
It depends on what your father is doing as a profession. If he is working under the table, he would have to show his income to the government if they ask him to, otherwise he is not following the law of the land of that country and its government. Most work overseas is done by a working visa and the person working is an immigrant of that country. If your father is selling alcohol or pork or illegal drugs to other people, then the income earned is haraam. If he is working for a hardware store or a construction company for building houses for people, then that's completely halal. I would need further insight to what work he is doing, but on the general level, if the job leads to haraam, such as working for a technology company that invests in Alcohol or inappropriate dress.
If the nature of work he is doing is halal then the income is also halal. Islam is not bound to the laws made by humans or governments.
Tomorrow some tyrant will make a law which will forbid people to take a bath. Would that make bathing in that country haram? No, ofcourse not.
So, as long as he is not doing anything that is haram according to the law of Islam like becoming a male prostitute, or a drug lord etc, then the income is halal.